EXAMPLE 2 Graphing Points in a Coordinate Plane SOLUTION Begin at the origin, move 4 units to the right, then 2 units down. Point A lies in Quadrant IV. a. b. Begin at the origin, move 1 unit to the left, then 2.5 units up. Point B lies in Quadrant II. a. A (4, –2) b. B (–1, 2.5) c. C (0, –3) Plot the point and describe its location.

EXAMPLE 2 Graphing Points in a Coordinate Plane c. Begin at the origin, move 3 units down. Point C lies on the y -axis.

EXAMPLE 3 Solve a Multi-Step Problem Archaeology On a field trip, students are exploring an archaeological site. They rope off a region to explore as shown. Identify the shape of the region and find its perimeter. The units on the scale are feet.

EXAMPLE 3 Solve a Multi-Step Problem SOLUTION STEP 1 Notice that points A, B, C, and D form a rectangle. Find the coordinates of the vertices. STEP 2 Find the horizontal distance from A to B to find the length l. x -coordinate of B x -coordinate of A = l – = –30 –60 = = 60 A(–30, 20), B(30, 20), C(30, –20), D (–30, –20)

EXAMPLE 3 Solve a Multi-Step Problem STEP 3 Find the vertical distance from A to D to find the width w. STEP 4 Find the perimeter: y -coordinate of D y -coordinate of A = w – = 20 – ( –20 ) 40 = = 2l + 2w = 2(60) + 2(40) = 200. ANSWER The region’s perimeter is 200 units 10 feet per unit = 2000 feet.

Plot the point and describe its location. 4. R (–3, 4) 5. S (1, –2.5) GUIDED PRACTICE for Examples 2 and 3 Begin at the origin and move 3 units to the left, then 4 units up. Point R lies in Quadrant II. Begin at the origin and move 1 unit right, then 2.5 units down. Point S lies in Quadrant IV.

Plot the point and describe its location. GUIDED PRACTICE for Examples 2 and 3 6. T (0.5, 3) 7. U (–3, 4) Begin at the origin and move 0.5 unit to the right, then 3 units up. Point T lies in Quadrant I. Begin at the origin and move 4 units to the left. Point U lies on the x-axis.

Plot the point and describe its location. GUIDED PRACTICE for Examples 2 and 3 8. Move points A and B in Example 3 to form a new rectangle. Find the perimeter. Answers may vary. Sample answer: Moving A and B to A( –30, 0 ) and B( 30, 0 ), the perimeter is 160 units. ANSWER